biosci220 midterm

NMDS (Non-metric Multidimensional Scaling)

A multivariate exploratory technique that preserves rank-order relationships among samples by placing them in a low-dimensional space; uses a distance matrix and iterative optimization with a nonparametric approach.

Distance matrix

A matrix of pairwise distances between samples (samples x samples) calculated from a chosen distance measure (e.g., Euclidean or Bray-Curtis).

Euclidean distance

Straight-line distance in multivariate space; appropriate when variables are on comparable scales; treats similar measurements as similar (e.g., penguin measurements).

Bray-Curtis distance

Distance based on counts/abundances commonly used for ecological community data; double zeros are less informative; used for macroinvertebrate orders data.

Rank order distance

NMDS uses the rank order of distances rather than their actual values, making the analysis nonparametric and less reliant on distributional assumptions.

Nonparametric

An approach with few or no distributional assumptions; reduces model assumptions in multivariate analyses.

Stress (Kruskal stress)

A goodness-of-fit measure for NMDS indicating how well the low-dimensional configuration matches the original distance structure; lower stress is better.

Dimensionality in NMDS

The number of dimensions in the NMDS solution (commonly 2 or 3); chosen a priori; higher dimensions reduce stress but are harder to visualize.

Scree plot

A diagnostic plot of stress versus the number of NMDS dimensions to help decide how many dimensions to retain.

MetaMDS

A function in the vegan package that performs NMDS on ecological data; handles distance options, random restarts, and returns an object with sample scores and variable scores.

Random restart

NMDS optimization starts from multiple random initial configurations to search for a low-stress solution; different restarts can converge to different minima.

Global minimum vs local minimum

The best overall solution across restarts is the global minimum; some restarts may converge to suboptimal local minima.

Positive data for NMDS / MinShift

MetaMDS requires nonnegative data; after standardization negative values can occur, so a minShift function shifts data to positive values.

Standardization (scale)

Centering data to zero mean and scaling to unit variance to remove unit differences and make variables comparable.

Penguins dataset (Palmer penguins)

A numeric dataset with four variables (bill length, bill depth, flipper length, body mass) used to illustrate NMDS; year is numeric but treated as categorical.

Macroinvertebrate orders dataset

Ecological community data with eight macroinvertebrate orders used to illustrate Bray-Curtis NMDS; counts; usually not standardized.

Sample scores

The coordinates (x, y) of samples in the NMDS plot, representing their position in reduced space.

Variable scores / Species scores

Coordinates indicating how original variables (or taxa) contribute to sample separation in NMDS.

Axis interpretability in NMDS

NMDS axes do not have inherent numerical meaning; only relative distances between points matter; rotations/reflections do not affect interpretation.

Dim check_MDS

A GOEVEJ package function that plots dimensions versus Kruskal stress to help decide how many NMDS dimensions to keep.

NMDS (Non-metric Multidimensional Scaling)

An ordinal, exploratory technique that uses a distance matrix and rank order to place samples in a low-dimensional space (usually 2–3D); focuses on the order of distances rather than their exact values.

Ordination

A method to arrange samples in a reduced-dimensional space to approximate the true relationships among samples; serves as a way to interpret multivariate data.

Distance Matrix

A matrix containing pairwise distances between samples (also called a resemblance matrix); used as input for NMDS and other ordination methods.

Bray-Curtis Dissimilarity

A 0–1 distance measure commonly used in biology that ignores double zeros and gives more weight to low-count differences; emphasizes presence/absence and relative abundances.

Euclidean Distance

The straight-line distance between two points (the “as the crow flies” metric); treats all differences numerically and includes double zeros in calculations.

Double Zero

A pair of samples sharing a zero value for a variable; in Euclidean distance, these zeros contribute to the similarity between samples regardless of context.

Rank Order in NMDS

NMDS uses the order of distances (ranks) rather than their absolute magnitudes to construct the low-dimensional configuration.

Stress (in NMDS)

A single-number goodness-of-fit metric (0 to 1) indicating how well the low-dimensional configuration represents the high-dimensional distances; lower is better.

Random Configuration

The initial, random placement of samples in the chosen low-dimensional space before NMDS optimization begins.

Gradient Analysis

The optimization step in NMDS where the configuration is iteratively adjusted along the steepest slope to improve fit.

Global Minimum vs Local Minimum

Global minimum is the best overall configuration; NMDS can get stuck in local minima, hence multiple restarts may be used to approach the global minimum.

Non-parametric

A property of NMDS indicating it relies on ranks rather than raw data values and does not assume a specific data distribution.

Dimensionality (k)

The number of axes (dimensions) in the NMDS plot; commonly 1–3 for visualization, with higher values harder to interpret.

Distance Measures in Biology

Various methods to compute dissimilarities; Euclidean and Bray-Curtis are common, and the choice affects the NMDS output.

Tidy Data

A clean, organized data format with variables as columns and observations as rows, enabling straightforward construction of distance matrices.

Data Cloud

A visual concept of how samples occupy high-dimensional space; NMDS represents this cloud in a lower-dimensional plot.

Two-Dimensional NMDS Plot

A visualization of samples in 2D after dimension reduction, used to interpret relationships and patterns among observations.

Intercept

The predicted value of the response when all predictors are zero; for categorical predictors, corresponds to the reference (baseline) category.

Slope

The change in the response for a one-unit change in a numeric predictor; in additive models, slopes are the same across groups.

Null model

An intercept-only model with no explanatory variables; estimates the overall mean and is analogous to a one-sample t-test.

Categorical explanatory variable

A qualitative predictor with distinct categories (e.g., penguin species) used in regression.

Dummy variables

0/1 indicators used to encode categorical predictors so each non-reference category has its own intercept.

Reference category

The baseline level of a categorical predictor against which other levels are compared in the model.

Additive model

A regression model where the effects of predictors add up with a common slope across groups; lines are parallel.

Interaction model

A model that includes interaction terms, allowing slopes to differ by category; lines are not parallel.

Dummy coding

Encoding scheme using 0/1 variables to represent categories and enable group-specific intercepts.

Linear model (LM)

A regression framework modeling a continuous response as a linear combination of predictors; t-tests and ANOVA are special cases.

ANOVA

A method to test for differences among means and to compare nested models in regression.

AIC (Akaike Information Criterion)

A model quality metric that balances goodness-of-fit with model complexity; lower is better; differences >~4 suggest meaningful improvement.

Parsimony

Preference for simpler models that sufficiently explain the data, balancing fit and complexity.

Confidence interval

A range around a parameter estimate that would contain the true parameter in repeated samples; a single study’s interval either contains it or not.

Shapiro-Wilk test

A normality test for residuals, used as an alternative or complement to QQ plots.

QQ plot

A diagnostic plot comparing observed quantiles to theoretical quantiles to assess normality of residuals.

Residuals

Differences between observed values and model-predicted values, used to assess fit and detect patterns or outliers.

Log transformation

Applying a logarithm to data to stabilize variance or meet model assumptions; not always effective.

Back-transformation

Transforming predictions from a transformed scale (e.g., log) back to the original scale for interpretation.

Non-independence

A violation of the assumption that observations are independent; may require alternative tests or models.

Population parameter

The true value of a quantity in the population (e.g., the true mean); estimated from sample data.

Point prediction

A single predicted value from the regression equation for a given set of predictor values.

Hypothesis testing

A framework for deciding if data provide evidence against a null hypothesis, often using p-values.

Palmer penguins data set

A convenient penguin measurements data set used in the course to practice hypothesis testing, regression, and inference.

Hypothesis testing

Process of evaluating evidence from data to decide whether to reject a null hypothesis.

Null hypothesis

Statement of no effect or no difference that is tested against by the data.

Alternative hypothesis

Statement that there is a difference or effect; at least one group mean differs.

p-value

Probability, under the null hypothesis, of obtaining results as extreme as observed; indicates strength of evidence against the null.

t statistic

Test statistic used in t-tests to assess differences between means (one-sample, paired, or two-sample).

Welch t test

A t-test variant that does not assume equal variances between groups; more robust when variances differ.

Student t test

Standard t-test assuming equal variances between groups.

ANOVA (one-way)

Analysis of Variance; tests whether three or more group means are equal using an F statistic.

F statistic / F value

Ratio of between-group variability to within-group variability; used to assess differences among group means.

Between-group variability

Variability due to differences between group means.

Within-group variability

Variability of observations within each group (also called error or residual variability).

Linear regression

Model describing the relationship between a predictor x and a response y with a line y = a + b x.

Intercept (a)

Predicted value of y when x = 0; often not biologically meaningful depending on x.

Slope (b)

Change in y per unit change in x; indicates direction and strength of the relationship.

Regression coefficients

Estimated intercept and slope parameters in a linear model.

Residual

Difference between an observed value and its model-predicted value (y - ŷ).

Normality assumption

Residuals are approximately normally distributed for valid inference.

Constant variance (homoscedasticity)

Residuals have constant spread across fitted values.

Model assumptions

Requirements for linear regression to be valid: independence, normality, and constant variance.

Model diagnostic plots

Plots (e.g., residuals vs fitted, scale-location, QQ plot) used to check regression assumptions.

QQ plot

Quantile-quantile plot used to assess normality of residuals against a normal distribution.

Scale-location plot

Plot used to assess homoscedasticity and potential nonlinearity in regression.

Residuals vs fitted plot

Plot used to detect non-constant variance or patterns in residuals.

Influential observation

Data point that disproportionately affects the regression line; detected via diagnostic plots.

R

Statistical software used to fit linear models (LM) and run ANOVA, computing p-values and other statistics.

LM (linear model) in R

Function to fit linear regression models and extract coefficients and diagnostics.

AOV in R

Function for performing analysis of variance; alternative to LM for ANOVA results.

Confidence interval

Range around an estimate that with a chosen level contains the true population parameter.

Randomization test

Nonparametric method that builds a null distribution by reshuffling labels.

Type I error

False positive: rejecting a true null hypothesis.

Type II error

False negative: failing to reject a false null hypothesis.

Bill length and bill depth (penguins example)

Bill length as predictor and bill depth as response in a linear model on penguin data.

Body mass and flipper length (penguins example)

Body mass as predictor and flipper length as response in a linear model on penguin data.

Categorical predictor coding in R

R encodes a categorical predictor with an intercept for the baseline level (alphabetically first) and coefficients for other levels.

Null distribution

Distribution of a test statistic assuming the null hypothesis is true.

What is data sovereignty?

The idea that data is governed by the laws of the country or region where it is stored; Indigenous data sovereignty expands this to the rights of Indigenous peoples over the collection, ownership, and use of their data; Māori data sovereignty is the New Zealand expression of these rights.

Is data neutral and objective in scientific practice?

No. Data is shaped by human choices and context; bias can enter during collection, experimental design, inclusion/exclusion, definitions, methods, funding, and power structures; data is not neutral.

What are the CARE principles?

Collective Benefit, Authority to Control, Responsibility, and Ethics; frameworks designed to ensure data practices respect Indigenous rights and interests.

How do CARE principles differ from FAIR principles?

FAIR focuses on the technical properties of data (Findable, Accessible, Interoperable, Reusable); CARE centers on the rights, governance, and benefits of Indigenous peoples in relation to data.